The operation of the architecture as a fault-tolerant quantum computer is underpinned by the concept that the logical error rate of an encoded computation can be arbitrarily lowered by increasing the size of the code.
This concept is based on the idea of fault-tolerance thresholds.
The existence of such thresholds for qubit-based architectures has been a subject of extensive research for over twenty years [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]} but the existence of thresholds for CV-based architectures [14]} is less well understood.
Furthermore, the question of whether hybrid architectures remain fault-tolerant with probabilistic sources of GKP qubits is not obvious.
Here we provide numerical evidence that our architecture does indeed have a threshold in the presence of errors arising from finite squeezing and for a range of swap-out probabilities.
As we detail in this section, in order to calculate the threshold, we simulate the hybrid architecture operating as a quantum memory and run a complete error-correction procedure [15]}.
We detail the various steps involved in the simulation of the thresholds in alg:ft.
